Problem: Solve for $x$ : $4\sqrt{x} + 1 = 6\sqrt{x} + 5$
Solution: Subtract $4\sqrt{x}$ from both sides: $(4\sqrt{x} + 1) - 4\sqrt{x} = (6\sqrt{x} + 5) - 4\sqrt{x}$ $1 = 2\sqrt{x} + 5$ Subtract $5$ from both sides: $1 - 5 = (2\sqrt{x} + 5) - 5$ $-4 = 2\sqrt{x}$ Divide both sides by $2$ $\frac{-4}{2} = \frac{2\sqrt{x}}{2}$ Simplify. $-2 = \sqrt{x}$ The principal root of a number cannot be negative. So, there is no solution.